A317623 Number of distinct values of X*(3*X-1) mod n.

1, 1, 3, 2, 3, 3, 4, 4, 9, 3, 6, 6, 7, 4, 9, 8, 9, 9, 10, 6, 12, 6, 12, 12, 11, 7, 27, 8, 15, 9, 16, 16, 18, 9, 12, 18, 19, 10, 21, 12, 21, 12, 22, 12, 27, 12, 24, 24, 22, 11, 27, 14, 27, 27, 18, 16, 30, 15, 30, 18, 31, 16, 36, 32, 21, 18, 34, 18, 36, 12, 36

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(2^e) = 2^(e-1), a(3^e) = 3^e, a(p^e) = 1 + floor( p^(e+1)/(2*p+2) ) for prime p >= 5.

Mathematica

f[2, e_] := 2^(e-1); f[3, e_] := 3^e; f[p_, e_] := 1 + Floor[p^(e+1)/(2*p+2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 13 2020 *)

Prog

(PARI) a(n)={my(v=vector(n)); for(i=0, n-1, v[i*(3*i-1)%n + 1]=1); vecsum(v)}
(PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); if(p<=3, if(p==2, 2^(e-1), 3^e), 1 + p^(e+1)\(2*p+2)))}

Crossrefs

Cf. A000224, A290731, A290732.

Sequence in context: A345755 A111114 A242409 * A286244 A230010 A230847

Adjacent sequences: A317620 A317621 A317622 * A317624 A317625 A317626

Keyword

nonn,mult

Author

Andrew Howroyd, Aug 01 2018

Status

approved